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Optimization of the Superconducting Linear Magnetic Bearing of a Maglev Vehicle



Considering the need for cost/performance prediction and optimization of superconducting maglev vehicles, we develop and validate here a 3D finite element model to simulate superconducting linear magnetic bearings. Then we reduce the 3D model to a 2D model in order to decrease the computing time. This allows us to perform in a reasonable time a stochastic optimization considering the superconductor properties and the vehicle operation. We look for the permanent magnet guideway geometry that minimizes the cost and maximizes the lateral force during a displacement sequence, with a constraint on the minimum levitation force. The displacement sequence reproduces a regular maglev vehicle operation with both vertical and lateral movements. For the sake of comparison, our reference is the SupraTrans prototype bearing. The results of the optimization suggest that the bearing cost could be substantially reduced, while keeping the same performances as the initial design. Alternatively, the performances could be significantly improved for the same original cost.
4014 12
PM guideway I
PM guideway C
PM guideway B
2714 18
PM guideway A
Optimization of the Superconducting Linear
Magnetic Bearing of a Maglev Vehicle
Loïc Quéval
, Guilherme G. Sotelo
, Y. Kharmiz
, Daniel H.N. Dias
, Felipe Sass
1 Lab for Electrical Machines, University of Applied Sciences, Düsseldorf, Germany.
2 Fluminense Federal University, Niterói (RJ), Brazil.
3 Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
Develop and validate a 3D FE model of a superconducting linear magnetic bearing.
Reduce the 3D model to a 2D model to decrease the computing time while keeping a good accuracy.
Use the 2D model to optimize the bearing cost considering a displacement sequence.
PM guideway model
We developed a superconducting linear magnetic bearing 3D finite element model. It is
based on the H-formulation with a power law E-J relationship. The J
(B) dependence, the PM
guideway real geometry and the iron nonlinearity are included. The model is validated by
comparison with experimental data. For the optimization, the 3D model is reduced to a 2D
model by shortening artificially its length, instead of decreasing the critical current density.
Taking the SupraTrans prototype bearing as reference, the PM guideway optimization results
show that it is possible to greatly reduce the cost for the same performances on a given
displacement sequence; or to greatly improve the performances for the same cost.
Víctor M.R. Zermeno
, Raimund Gottkehaskamp
ID: 3A-LS-P-04.03
From 3D to 2D
It is common practice to calibrate the critical current density J
of the bulk using the
maximum levitation force measured during the ZFC sequence.
We consider the bearing initially designed and optimized for the SupraTrans maglev vehicle
HTS bulk model
SLMB model
(a) Zero field cooling
(b) Vertical displacement downward
(c) Vertical displacement upward.
(a) Field cooling
(b) Vertical displacement downward
(c) Lateral displacements.
What: Permanent magnets and iron pieces
arranged in flux concentrator.
How: 2D magnetostatic FEM
- iron nonlinear BH curve
- real geometry.
What: 3-seeded melt-textured YBCO block.
How: 2D or 3D H-formulation FEM
- power law E-J relationship
- isotropic Kim like model Jc(B)
- 3 independent domains.
How: Unidirectional coupling between HTS bulk
model and PM guideway model.
- only 1 static solution of the PM guideway model
- reduced LN
domain around HTS bulk.
Objective and constraints
3D model 2D model
with reduced J
with reduced d
2D model
Dimensions of PM guideway : 4 parameters
Dimensions of HTS bulk : unchanged
Computing time < 1 min
We look for the PM guideways that minimize the cost of the guideway and maximize the
lateral force during LD sequence, with a constraint on the minimum levitation force,
Multi-objective Particule Swarm Optimization (PSO)
- 100 particules
- 25 generations
Total computing time ~40 h
Optimization algorithm
Fig. 1 - SLMB Geometry.
Fig. 2 - Magnetic flux density above the PM guideway
at z = 1, 5, 10, 20 mm.
Fig. 3 - Levitation force for ZFC sequence.
Fig. 4 - Lateral force for LD sequence.
Fig. 5 - Levitation force for LD sequence.
Note: The decrease of the levitation force during lateral displacements should be taken into
account during the optimization.
"Optimization on a displacement sequence"
5 mm
ZFC sequence
LD sequence
5 mm
25 mm 100 mm
10 mm
Fig. 8 - Initial and optimized PM guideways.
Dimensions in mm (on scale).
where , , .
cost [€/m]
PM guideway I
PM guideway A
PM guideway B
PM guideway C
-23 %
+38 %
Fig. 7 - Bi-objective optimization results.
Fig. 6 - Parametrization of the PM guideway.
ac d
... As one of the important applications, HTS maglev has received extensive attention from researchers. More theoretical research and test line constructions have been developed in Russia [7], Germany [8], Italy [9], Brazil [10], Japan [11], France [12], UK [13], and China [4,14]. ...
... However, two issues should not be ignored. Firstly, most of these models use two-dimensional forms as a simplification of three-dimensional (3D) entities [12,18,19], or use rotationally symmetrical boundary conditions to simulate cylindrical bulks [24]. These models cannot simulate the bulks in various combinations with the characteristics of longitudinal placement. ...
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... where J C0 , T C and B 0 are constants determined by the property of the material. In this paper, time-dependent magnetic field is calculated by unidirectional coupling model between the PM and the superconductor which is built by Sass [21] and Quéval [22]. In this model, the coordinates are not time dependent, allowing the use of a fixed mesh, which will lead to a more accurate result. ...
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... Optimization of a linear bearing was performed to minimize the cost and maximize the lateral force [93]. The bearing was modeled using H formulation with power-law E-J relationship. ...
Magnetic bearings are being researched for high-speed applications, such as flywheel energy storage devices, to eliminate friction losses. As per Earnshaw's theorem, stable levitation cannot be achieved for a static passive magnetic bearing system. Fully passive stable levitation can be achieved with the help of superconducting magnetic bearings (SMB). This article provides an in-depth review of the modeling, analysis, and development of SMB. The different SMB configurations are highlighted, together with essential methodologies for estimating and improving their performance. The advancements in mathematical models used and the optimization of bearing characteristics are thoroughly discussed. Further, key developments in the application of SMB in flywheel energy storage systems are also reviewed.
... Work on optimizing the superconducting linear magnetic bearing of a maglev vehicle was presented [5]. A multiobjective multi-constraint optimization to minimize the cost or volume of the 3D bearing geometry, considering variable component dimensions and spacing, was initially performed in [6]. ...
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Persistent currents induced in hard superconductors (HSC) were ; investigated by measuring the resulting magnetic effects. The tubular HSC ; examined were Nb powder, NbâSn, and 3Nb- Zr samples of uniform wall ; thickness and length large compared to the diameter. Experimental evidence is ; presented that in HSC the Lorentz force plays a crucial role in determining the ; critical current density and the critical persistent currents in decay with a ; measurable rate. (H.D.R.);
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